Related papers: Schrodinger-Newton wave mechanics. The model
We develop the idea that, as a result of the arbitrariness of the factor ordering in Wheeler-DeWitt equation, gauge phases can not, in general, being completely removed from the wave functional in quantum gravity. The latter may be…
We propose a stochastic modification of the Schr\"{o}dinger-Newton equation which takes into account the effect of extrinsic spacetime fluctuations. We use this equation to demonstrate gravitationally induced decoherence of two gaussian…
We consider the stochastic nonlinear Schroedinger equation driven by a multiplicative noise in a semiclassical regime, where the Plank constant is small. In this regime, the solution of the equation exhibits high-frequency oscillations. We…
We modify the Schr\"{o}dinger equation in a way that preserves its main properties but makes use of higher order derivative terms. Although the modification represents an analogy to the Doebner-Goldin modification, it can differ from it…
The wave equation for spin-0 massless particles with the Lorentz violating term leading to varying speed of particles is considered. This equation is represented as the first-order 6$\times$6 matrix equation. Solutions of the equation in…
We consider the propagation of strong gravitational waves interacting with a nonperturbative vacuum of spinor fields. To described the latter, we suggest an approximate model. The corresponding Einstein equation has the form of the…
Newton's second law may be used to obtain a wave equation, which reduces to Schrodinger's equation in the nonrelativistic limit and for a conservative force.
Spinless Salpeter equation for two bound particles is analyzed. We use the fact that in relativistic kinematics the spatial two particle relative momentum is relativistic invariant. Free particle hypothesis for the bound state is developed:…
The Schr\"odinger-Newton [SN] equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the…
Schrodinger's equation for a single particle is proved from the assumption that dynamics can be formulated in a space whose curvature is the electromagnetic force.
It is well-known that the coordinate as a continuous variable, consisting of a set of all points between 0 and $L$ contradicts the observability of measurement. In other words there might exist a fundamental length in nature, such as the…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
The nonlinear Schr\"odinger-Newton equation, a prospective semiclassical alternative to a quantized theory of gravity, predicts a gravitational self-force between the two trajectories corresponding to the two z-spin eigenvalues for a…
A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is…
Specific solutions of the nonlinear Schr\"odinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is, whether these solutions also exist in the…
In the standard approach to defining a Planck scale where gravity is brought into the quantum domain, the Schwarzschild gravitational radius is set equal to the Compton wavelength. However, ignored thereby are the charge and spin, the…
Basing on the fundamental symmetry that the space-time inversion is equivalent to particle-antiparticle transformation, a relativistic modification on the stationary Schrodinger equation for many-particle system is made. The eigenvalue in…
We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing…
It is well known that the Schr\"odinger equation is only suitable for the particle in common potential $V(\vec{r},t)$. In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave…
We study the massless limit of the Klein-Gordon (K-G) equation in 1+1 dimensions with static complex potentials as an attempt to give an alternative, but equivalent, representation of plane electromagnetic (em) wave propagation in active…